Uncategorized: Practice Problem & Solution
A ship A is moving Westwards with a speed of \(10 text{ km/h}text{ and a ship B 100 km South of A, is moving Northwards with a speed of 10 km/h. The time after which the distance between them becomes shortest, is: (2015)}\
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
Concept: Relative velocity for minimum distance between moving objects.
Formula: \(t = -(vec{r_{rel}} cdot vec{v_{rel}}) / v_{rel}^2\).
\(vec{v_A} = -10 hat{i}\), \(vec{v_B} = 10 hat{j}\). \(vec{v_{BA}} = 10 hat{i} + 10 hat{j}\).
Initial relative position \(vec{r_{BA}}(0) = -100 hat{j}\).
\(t = -((-100 hat{j}) cdot (10 hat{i} + 10 hat{j})) / (10^2 + 10^2) = -(-1000) / 200 = 5 text{ h}\).
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